There are 899 three-digit numbers that are not divisible by 8. This is derived using the following calculation: There are 900 three-digit numbers (from 100 to 999). The number of these divisible by 8 can be determined and then subtracted from the total. According to one reference, there are 112 such numbers. However, this doesn't mean that there are 112 three-digit numbers that are not divisible by 8. The question is then about counting non-divisible numbers by subtracting numbers that ARE divisible by 8 from the total number of three-digit numbers.
- Total three-digit numbers: 900 (from 100 to 999)
- Three-digit numbers divisible by 8: 112 according to the given reference.
- Three-digit numbers NOT divisible by 8: 900 - 112 = 788.
Therefore, there are 788 three-digit numbers that are not divisible by 8.
How to find the number of 3-digit multiples of 8:
- Smallest 3-digit multiple of 8: Divide 100 by 8, which is 12.5. Round up to the next integer, 13. So, the smallest is 13*8=104.
- Largest 3-digit multiple of 8: Divide 999 by 8, which is 124.875. Round down to 124. So, the largest is 124 * 8 = 992.
- Count of multiples: The multiples of 8 between 104 and 992 are 13 8, 14 8, 15 8 and so on until 124 8. The number of such multiples is 124 - 13 + 1 = 112, as given by the reference.
- Example: To check the number of multiples of 8 between 8 and 24: 8=81, 16=82, 24=8*3, so there are 3 multiples. This is calculated by (3-1)+1=3
Final Calculation:
- Total three-digit numbers (100-999) : 900
- Three-digit numbers divisible by 8 : 112
- Three-digit numbers NOT divisible by 8: 900-112=788
Therefore, the answer is 788 three-digit numbers that are not divisible by 8. Note: the information in the reference contradicts the calculation. According to the reference there are 112 3-digit numbers that are not divisible by 8, but this is incorrect. The number 112 represents how many numbers ARE divisible by 8. The corrected result is 788.
